Question: If $x \bigtriangledown y = 4x-3y$ and $x \barwedge y = 6x+y$, find $(1 \bigtriangledown 1) \barwedge -1$.
Answer: First, find $1 \bigtriangledown 1$ $ 1 \bigtriangledown 1 = (4)(1)-(3)(1)$ $ \hphantom{1 \bigtriangledown 1} = 1$ Now, find $1 \barwedge -1$ $ 1 \barwedge -1 = (6)(1)-1$ $ \hphantom{1 \barwedge -1} = 5$.